reading this thread I am starting to feel that the whole world is a tuxedo and I'm a pair of brown shoes.
I use foam for most of my framed work. I use a 4-ply 100% cotton rag overmat and buffered foamcore backing. I do not dry mount my work - I use my press to flatten and, in the case of bromoil, to super dry. I use archival dots at the top corners of the print to secure it to the backing and four more to secure the overmat to the backing.
I used to use the same mat board for backing and overmat but find that with the aluminum frames I use that the additional thickness of the foamcore provides a tighter, flatter fit.
I should note that probably 80% of my prints 5x7 on 8x10 paper. This small size may account for my lack of problems with foamcore though I have a few larger prints mounted and framed at 20x24 with foamcore and have not noticed a problem.
If I am going to present the work as matted with an overmat, I still use the same 4-ply for both.